Learning from
Principal Components Analysis of Residuals

The Rasch model extracts from observational data the linear dimension
best supported by those data. But each observation, to some degree, contains
its own characteristic features. These contradict the dimension. The
responses idiosyncratic characteristics are
manifested as the differences between what the Rasch model predicts and what
is observed, i.e., the observation residuals. Principal components analysis
of these residuals identifies characteristics shared in common among items.
These are often indications of secondary structures or sub-dimensions within
the data.

In this presentation, an analysis of an Attitudes to Recreational Drugs
survey is performed. This
identifies "for" and "against" statements. Further, it
confirms an earlier finding about that "for" and "against" are not always
perceived as opposite. More subtle sub-dimensions are also identified
in the instrument.

In this example, the power and utility of Principal Components analysis
of Rasch residuals is demonstrated.